This invention arose from the need to achieve rigidly-stable positioning of objects with 10 nanometer resolution and precision at low cost. In particular, an XYØ positioning stage that meets these criteria was required for precise mask-to-substrate alignment in a low-cost, submicron contact-lithography apparatus. [J. G. Goodberlet and Bryan L. Dunn, Microelectronic Eng., Vol. 53, p. 95 (2000).] In most contact lithography instruments, including those used for nano-imprint lithography [S. Y. Chou, et al, Applied Physics Letters, Vol. 67, p. 3114 (1995).] and step-and-flash lithography [T. Bailey, et al, Journal of Vacuum Science and Technology B, Vol. 18, p. 3572 (2000)], significant forces and loads can act upon the stage after precise alignment has been achieved, thereby necessitating a need for a rigidly-stable platform. Although there exist several types of stages and positioning instruments, available commercially and under development, none exhibit the combined features of stability, high resolution, high precision and low cost required for this lithographic application. Positioning stages which achieve the resolution and precision requirements are prohibitively expensive because of their sophisticated mechanical and electronic components. Therefore, a need exists for an apparatus which demonstrates rigidly-stable positioning with 10-nm-level resolution and precision, and can be manufactured at low cost. In order to achieve this objective, it was necessary to innovate both a high-precision actuating element, which could be incorporated into the positioning stage, and a suitable stage design.